1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was b0e60a113750ca2637ec52c0391763ecf8851ace.

2 Data

Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here. We filter out countries with populations of greater than 500 000. Weeks where the deaths or cases are not greater than 50 are left out of results.

5 Results

5.1 Current \(R_{t,m}\) estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.1.0.1 Cases

5.1.1 Deaths

5.2 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.2.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Brazil deaths 1,032 2020-11-09 0.4 0.4 0.4
Paraguay deaths 72 2020-11-09 0.6 0.7 0.9
Costa_Rica deaths 79 2020-11-09 0.6 0.7 0.9
Bolivia deaths 64 2020-11-09 0.6 0.7 0.9
Moldova deaths 93 2020-11-09 0.7 0.8 1.0
Libya deaths 58 2020-11-09 0.7 0.9 1.1
Israel deaths 120 2020-11-09 0.7 0.9 1.0
Bangladesh deaths 126 2020-11-09 0.8 0.9 1.0
Guatemala deaths 83 2020-11-09 0.7 0.9 1.1
Argentina deaths 2,420 2020-11-09 0.9 0.9 1.0

5.2.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Brazil cases 44,320 2020-11-09 0.3 0.4 0.4
Cote_dIvoire cases 116 2020-11-09 0.4 0.4 0.5
Belgium cases 49,562 2020-11-09 0.5 0.5 0.6
Honduras cases 2,296 2020-11-09 0.6 0.7 0.7
Sweden cases 13,126 2020-11-09 0.6 0.7 0.7
Guinea cases 231 2020-11-09 0.6 0.7 0.8
Bolivia cases 642 2020-11-09 0.7 0.7 0.8
Ireland cases 3,392 2020-11-09 0.7 0.8 0.8
Australia cases 63 2020-11-09 0.6 0.8 1.0
Netherlands cases 50,136 2020-11-09 0.8 0.8 0.8

5.2.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Sudan deaths 278 2020-11-09 631.0 881.1 1,269.4
Greece deaths 149 2020-11-09 1.6 2.0 2.4
Kosovo deaths 67 2020-11-09 1.5 1.9 2.5
Slovakia deaths 132 2020-11-09 1.3 1.6 2.0
Slovenia deaths 146 2020-11-09 1.3 1.6 2.0
Serbia deaths 64 2020-11-09 1.2 1.5 1.9
Croatia deaths 232 2020-11-09 1.3 1.5 1.7
Italy deaths 2,568 2020-11-09 1.3 1.4 1.6
Bulgaria deaths 367 2020-11-09 1.2 1.4 1.6
Austria deaths 221 2020-11-09 1.2 1.4 1.6

5.2.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Sudan cases 271 2020-11-09 2.2 2.7 3.3
Cameroon cases 628 2020-11-09 2.0 2.2 2.5
Ghana cases 1,078 2020-11-09 1.5 1.7 2.0
Madagascar cases 112 2020-11-09 1.4 1.7 1.9
Botswana cases 1,193 2020-11-09 1.3 1.6 2.1
Estonia cases 1,140 2020-11-09 1.5 1.6 1.8
Somalia cases 288 2020-11-09 1.2 1.6 2.2
Lithuania cases 8,980 2020-11-09 1.4 1.5 1.6
Algeria cases 3,779 2020-11-09 1.4 1.5 1.6
Zimbabwe cases 157 2020-11-09 1.3 1.5 1.7

5.3 Country Plots by Continent

Below we plot results for each country/province in a list. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds five.

5.3.1 Africa

5.3.1.1 Algeria

5.3.1.2 Angola

5.3.1.3 Benin

5.3.1.4 Botswana

5.3.1.5 Burkina_Faso

5.3.1.6 Burundi

5.3.1.7 Cameroon

5.3.1.8 Cape_Verde

5.3.1.9 Central_African_Republic

5.3.1.10 Chad

5.3.1.11 Comoros

5.3.1.12 Congo

5.3.1.13 Cote_dIvoire

5.3.1.14 Democratic_Republic_of_the_Congo

5.3.1.15 Djibouti

5.3.1.16 Egypt

5.3.1.17 Equatorial_Guinea

5.3.1.18 Eswatini

5.3.1.19 Ethiopia

5.3.1.20 Gabon

5.3.1.21 Gambia

5.3.1.22 Ghana

5.3.1.23 Guinea

5.3.1.24 Guinea_Bissau

5.3.1.25 Kenya

5.3.1.26 Lesotho

5.3.1.27 Liberia

5.3.1.28 Libya

5.3.1.29 Madagascar

5.3.1.30 Malawi

5.3.1.31 Mali

5.3.1.32 Mauritania

5.3.1.33 Mauritius

5.3.1.34 Morocco

5.3.1.35 Mozambique

5.3.1.36 Namibia

5.3.1.37 Niger

5.3.1.38 Nigeria

5.3.1.39 Rwanda

5.3.1.40 Senegal

5.3.1.41 Sierra_Leone

5.3.1.42 Somalia

5.3.1.43 South_Africa

5.3.1.44 South_Sudan

5.3.1.45 Sudan

5.3.1.46 Togo

5.3.1.47 Tunisia

5.3.1.48 Uganda

5.3.1.49 United_Republic_of_Tanzania

5.3.1.50 Western_Sahara

5.3.1.51 Zambia

5.3.1.52 Zimbabwe

5.3.2 America

5.3.2.1 Argentina

5.3.2.2 Bolivia

5.3.2.3 Brazil

5.3.2.4 Canada

5.3.2.5 Chile

5.3.2.6 Colombia

5.3.2.7 Costa_Rica

5.3.2.8 Cuba

5.3.2.9 Dominican_Republic

5.3.2.10 Ecuador

5.3.2.11 El_Salvador

5.3.2.12 Guatemala

5.3.2.13 Guyana

5.3.2.14 Haiti

5.3.2.15 Honduras

5.3.2.16 Jamaica

5.3.2.17 Mexico

5.3.2.18 Nicaragua

5.3.2.19 Panama

5.3.2.20 Paraguay

5.3.2.21 Peru

5.3.2.22 Puerto_Rico

5.3.2.23 Suriname

5.3.2.24 Trinidad_and_Tobago

5.3.2.25 United_States_of_America

5.3.2.26 Uruguay

5.3.2.27 Venezuela

5.3.3 Asia

5.3.3.1 Afghanistan

5.3.3.2 Bahrain

5.3.3.3 Bangladesh

5.3.3.4 Bhutan

5.3.3.5 Cambodia

5.3.3.6 China

5.3.3.7 India

5.3.3.8 Indonesia

5.3.3.9 Iran

5.3.3.10 Iraq

5.3.3.11 Israel

5.3.3.12 Japan

5.3.3.13 Jordan

5.3.3.14 Kazakhstan

5.3.3.15 Kuwait

5.3.3.16 Kyrgyzstan

5.3.3.17 Lebanon

5.3.3.18 Malaysia

5.3.3.19 Maldives

5.3.3.20 Mongolia

5.3.3.21 Myanmar

5.3.3.22 Nepal

5.3.3.23 Oman

5.3.3.24 Pakistan

5.3.3.25 Palestine

5.3.3.26 Philippines

5.3.3.27 Qatar

5.3.3.28 Saudi_Arabia

5.3.3.29 Singapore

5.3.3.30 South_Korea

5.3.3.31 Sri_Lanka

5.3.3.32 Syria

5.3.3.33 Taiwan

5.3.3.34 Tajikistan

5.3.3.35 Thailand

5.3.3.36 Turkey

5.3.3.37 United_Arab_Emirates

5.3.3.38 Uzbekistan

5.3.3.39 Vietnam

5.3.3.40 Yemen

5.3.4 Europe

5.3.4.1 Albania

5.3.4.2 Armenia

5.3.4.3 Austria

5.3.4.4 Azerbaijan

5.3.4.5 Belarus

5.3.4.6 Belgium

5.3.4.7 Bosnia_and_Herzegovina

5.3.4.8 Bulgaria

5.3.4.9 Croatia

5.3.4.10 Cyprus

5.3.4.11 Czechia

5.3.4.12 Denmark

5.3.4.13 Estonia

5.3.4.14 Finland

5.3.4.15 France

5.3.4.16 Georgia

5.3.4.17 Germany

5.3.4.18 Greece

5.3.4.19 Hungary

5.3.4.20 Ireland

5.3.4.21 Italy

5.3.4.22 Kosovo

5.3.4.23 Latvia

5.3.4.24 Lithuania

5.3.4.25 Luxembourg

5.3.4.26 Moldova

5.3.4.27 Montenegro

5.3.4.28 Netherlands

5.3.4.29 North_Macedonia

5.3.4.30 Norway

5.3.4.31 Poland

5.3.4.32 Portugal

5.3.4.33 Romania

5.3.4.34 Russia

5.3.4.35 Serbia

5.3.4.36 Slovakia

5.3.4.37 Slovenia

5.3.4.38 Spain

5.3.4.39 Sweden

5.3.4.40 Switzerland

5.3.4.41 Ukraine

5.3.4.42 United_Kingdom

5.3.5 Oceania

5.3.5.1 Australia

5.3.5.2 New_Zealand

5.3.5.3 Papua_New_Guinea

## Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] European Centre for Disease Prevention and Control, “Data on the geographic distribution of COVID-19 cases worldwide.” European Union, 2020 [Online]. Available: https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide